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Copy file name to clipboardExpand all lines: Manuals/FDS_Technical_Reference_Guide/Radiation_Chapter.tex
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@@ -335,9 +335,9 @@ \subsection{Radiation Contribution to Energy Equation}
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\subsection{Correction of the Emission Source Term}
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In calculations of limited spatial resolution, the source term, $I_{\rm b}$, defined in Eq.~(\ref{emission_source_term}) requires special treatment in the flaming region of the fire. Typical FDS calculations use grid cells that are tens of centimeters in size, and consequently the computed temperatures constitute a bulk average for a given grid cell and are considerably lower than the maximum temperature in a diffusion flame. Because of its fourth-power dependence on the temperature, the source term must be modeled in those grid cells where combustion occurs. Elsewhere, the computed temperature is used directly to compute the source term. It is assumed that this ``flaming region'' is where the local, nominal radiative loss is greater than a specified lower bound, $\chi_{\rm r} \dq'''>10$~kW/m$^3$. In this region, the global radiative fraction model is used. The emission source term is multiplied by a corrective factor, $C$:
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In calculations of limited spatial resolution, the source term, $I_{\rm b}$, defined in Eq.~(\ref{emission_source_term}) requires special treatment in the flaming region of the fire. Typical FDS calculations use grid cells that are tens of centimeters in size, and consequently the computed temperatures constitute a bulk average for a given grid cell and are considerably lower than the maximum temperature in a diffusion flame. Because of its fourth-power dependence on the temperature, the source term must be modeled in those grid cells where combustion occurs. Elsewhere, the computed temperature is used directly to compute the source term. It is assumed that this ``flaming region'' is where the local, nominal radiative loss is greater than a specified lower bound, $\chi_{\rm r} \dq'''>1$~kW/m$^3$. In this region, the global radiative fraction model is used. The emission source term is multiplied by a corrective factor, $C$:
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\be I_{\rm b,f}(\bx) = C \,\frac{\sigma\, T(\bx)^4}{\pi} \quad ; \quad
When the source term defined in Eq.~(\ref{corrected_emission_source_term}) is substituted into Eq.~(\ref{net_emission}), the net radiative emission from the flaming region becomes the desired fraction of the total heat release rate. Note that this correction factor is bounded below by 0.1 and above by 100. These bounds are somewhat arbitrary, meant to prevent spurious behavior at the start of a simulation.
In its normal operation, the RTE transfers energy from hot, emitting gases, like flames, to colder, absorbing gases like water vapor or soot particulate. The absorption coefficient, $\kappa$, computed using RadCal, governs both the emission and absorption of thermal radiation. Because flame temperatures are not well-resolved for typically large-scale fire simulations, the source term in the RTE is adjusted in grid cells for which the radiative fraction, $\chi_{\rm r}$, times the local heat release rate per unit volume, $\dot{q}'''$, is greater than 10~kW/m$^3$
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In its normal operation, the RTE transfers energy from hot, emitting gases, like flames, to colder, absorbing gases like water vapor or soot particulate. The absorption coefficient, $\kappa$, computed using RadCal, governs both the emission and absorption of thermal radiation. Because flame temperatures are not well-resolved for typically large-scale fire simulations, the source term in the RTE is adjusted in grid cells for which the radiative fraction, $\chi_{\rm r}$, times the local heat release rate per unit volume, $\dot{q}'''$, is greater than 1~kW/m$^3$
The adjustment ensures that the net radiative emission from the combusting region (i.e. the fire) is the specified \ct{RADIATIVE_FRACTION} multiplied by the total combustion energy generated in this region. Elsewhere, hot and cold gases emit and absorb thermal radiation according to their bulk temperature and radiative properties, in particular the absorption coefficient, $\kappa$.
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The net radiative loss from the computational domain is reported as a function of time in the column \ct{Q_RADI} in the output file \ct{CHID_hrr.csv}. The absolute value of \ct{Q_RADI} divided by the total heat release rate, \ct{HRR}, is usually not exactly equal to the specified \ct{RADIATIVE_FRACTION}. The reason for this is that the specified radiative fraction of the fire's energy can be reabsorbed by colder combustion products such as smoke and water vapor, thereby decreasing the absolute value of \ct{Q_RADI}. Or, hot layer smoke and combustion products can heat up and emit thermal radiation, adding to the absolute value of \ct{Q_RADI}.
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The correction factor that is applied to the RTE source term in the region defined by Eq.~(\ref{clip}) by default is bound between 1 and 100, meaning that the correction factor only increases the net radiative output of the combusting region, if necessary, to achieve the desired \ct{RADIATIVE_FRACTION}. However, you can change the default behavior of the correction as follows. First, you can force the RTE source term to be modified in all grid cells by changing the 10 in Eq.~(\ref{clip}) to -1 via \ct{QR_CLIP} on the \ct{RADI} line, in which case the solver will apply the radiative fraction to the entire domain, not just the cells where combustion occurs. This will essentially force the net radiative loss from the entire domain to obey the \ct{RADIATIVE_FRACTION}. Second, you can allow the RTE source term to increase or decrease in value to achieve the desired \ct{RADIATIVE_FRACTION} by changing the lower limit of the correction factor, \ct{C_MIN}, from its default value of 1 to, say, 0.5 on the \ct{RADI} line. The corresponding parameter, \ct{C_MAX}, limits the correction factor to 100. The time-varying correction factor can be output using a device with quantity \ct{RTE SOURCE CORRECTION FACTOR}. Since \ct{RTE SOURCE CORRECTION FACTOR} is a global value, the position of the device does not matter.
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The correction factor that is applied to the RTE source term in the region defined by Eq.~(\ref{clip}) by default is bound between 1 and 100, meaning that the correction factor only increases the net radiative output of the combusting region, if necessary, to achieve the desired \ct{RADIATIVE_FRACTION}. However, you can change the default behavior of the correction as follows. First, you can force the RTE source term to be modified in all grid cells by changing the 1 in Eq.~(\ref{clip}) to -1 via \ct{QR_CLIP} on the \ct{RADI} line, in which case the solver will apply the radiative fraction to the entire domain, not just the cells where combustion occurs. This will essentially force the net radiative loss from the entire domain to obey the \ct{RADIATIVE_FRACTION}. Second, you can allow the RTE source term to increase or decrease in value to achieve the desired \ct{RADIATIVE_FRACTION} by changing the lower limit of the correction factor, \ct{C_MIN}, from its default value of 1 to, say, 0.5 on the \ct{RADI} line. The corresponding parameter, \ct{C_MAX}, limits the correction factor to 100. The time-varying correction factor can be output using a device with quantity \ct{RTE SOURCE CORRECTION FACTOR}. Since \ct{RTE SOURCE CORRECTION FACTOR} is a global value, the position of the device does not matter.
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